Abstract
Nanowires (NWs) are filamentary crystals with diameters of tens of nanometers and lengths of few microns. Semiconductor NWs have recently attracted a great interest, because they are emerging as building blocks for novel nanoscale devices. Since physical properties are size dependent, NWs display novel properties with respect to their bulk counterparts. Raman scattering is a nondestructive inelastic light scattering technique enabling the assessment of fundamental properties of NWs, such as crystal phase, electronic band structure, composition, and strain field. Here, we summarize the basic principles of Raman spectroscopy and measurement setup, with focus on the scattering geometries typically used for NWs. We show that changing experimental conditions, such as light polarization, excitation energy, and pressure, allows gaining information on specific NW properties, even in a spatially resolved manner along the NW length. As examples, we discuss Ge and GaAs NWs to highlight some differences between Raman spectra of NWs and the bulk, GaAs NWs to show how Raman permits to establish the crystal phase, and InGaAs/GaAs core/shell nanoneedles to explain how compositional homogeneity and strain field can be addressed by Raman spectroscopy. Finally, we discuss resonant Raman experiments on wurtzite InAs NWs that allowed the determination of their electronic band structure.
Keywords
- inelastic light scattering
- semiconductor nanowires
- crystal phases
- compositional disorder
- strain
- resonant Raman spectroscopy
1. Introduction: the world of nanowires
Semiconductor nanowires (NWs) are promising structures in the field of nanoscience. The name nanowire derives from the filamentary shape of these nanostructures. Indeed, they have two dimensions in the range of few to tens of nanometers, while the third dimension is much longer, in the micrometer range. Typical NWs with a filamentary shape are shown in Figure 1(a). The gold nanoparticles, which act as catalyzers during the growth, are clearly visible.
In 1991, K. Hiruma et al. accidentally grew InAs nanowires on GaAs substrates [1]. Since the time, when the word “nanowire” first appeared in a paper, NWs have attracted interest from a large number of scientists around the world owing to the extraordinary opportunities that they enable. In fact, NWs are smaller than bulk crystals and larger than nanocrystals, thus providing a natural bridge between macroscopic and microscopic worlds in both research and technology fields. Moreover, due to the anisotropic shape of NWs and their high surface‐to‐volume ratio, finite‐size and surface/interface effects are more important than the (more known) quantum confinement effects, a circumstance that renders NWs an ideal platform for the discovery of a variety of novel phenomena.
Semiconductor NWs can exist in many different chemical compositions, structures, and shapes. Regarding the chemical composition, NWs can be made by elemental semiconductors like Si and Ge, or by III–V compounds (e.g., GaAs), II–VI compounds (e.g., CdSe), III–V alloys (e.g., InGaAs), III‐nitrides (e.g., GaN), oxides (e.g., ZnO), etc. Not only homogeneously composed NWs exist, but also different materials can be mixed together in the same NW to form heterostructured NWs. Heterostructures are typically prepared in two ways [2]. In radial structures, one or more materials are grown around a NW, in a so‐called core‐shell or core‐multishell arrangement. Figure 1(b) shows a schematic of this kind of structures along with a scanning electron microscope image (SEM) of an InAs‐GaSb core‐shell NW and a cross‐section transmission electron microscopy (TEM) image of a core‐multishell GaAs/AlGaAs NW. In axial structures, the NW composition is varied along the NW main axis, as depicted in Figure 1(c), whereas an SEM image of an InP/InAs/InSb axial heterostructure is also displayed [3]. In the NW form, highly mismatched materials can grow on top of each other without misfit dislocations, due to the NW capability to accommodate strain by a coherent expansion of the lattice outward.
Regarding the shape, NWs have been grown in many different, sometimes funny, shapes that could add functionalities to nanoscale devices [4]. For instance, NWs were grown in branched or flower‐like morphologies [5], where an increased surface area ensures higher power‐conversion efficiency compared to straight and vertical NWs.
NWs are the nanomaterial system in which pivotal key parameters, such as composition, structure, morphology, and doping, have been best controlled to date. At the heart of this control is the development of successful methods for NW growth. In the top‐down technology, lithographic techniques allow to carve the nanowire structure out of a bulk material. This kind of approach ensures fine control over the position of the NWs, but the crystal quality of the NWs is not excellent (due to the surface damage produced by etching processes), and large‐area production is problematic and expensive. Therefore, bottom‐up NW fabrication is the most diffused. Since one‐dimensional growth on a substrate is not energetically favored with respect to a two‐dimensional growth, a change of the initial surface/interface is required to activate the NW growth. This change can be done by creating holes in the substrate (selective area growth) or by using metal particles, such as gold, to induce the crystal growth (particle‐assisted growth) via the so‐called “vapor‐liquid‐solid” (VLS) mechanism that was first invoked in the 1960s to explain the growth of Si whiskers [6]. In both cases, epitaxial techniques are employed to fabricate NWs. In Figure 2, the main steps of a typical VLS growth process leading to free‐standing III–V NWs are explained, since this is the most widely used technique to grow high‐quality nanowires. Each gold droplet represents the nucleation site of a NW, so there are approximately as many NWs as the droplets are. The gold droplets can be directly deposited on the substrate or result from the annealing of an Au thin film. To achieve a perfect control on the NW position, an array of gold particles can be even prepared by using lithography techniques.
Thanks to the high degree of control reached on the NW growth process, nowadays most of NW properties can be finely tuned, to such an extent that the creation of NWs tailor fit to specific applications is close to be achieved. Due to the several technological applications enabled by NWs, the interest of the scientific community on them is rapidly growing, as testified by the exponentially growing number of papers published on NWs in the last two decades. The field where the peculiar shape and dimensions of NWs have revealed to have great potential in enabling new functions and/or simply enhancing performances of existing devices is very broad, as it includes electronics, photonics, biosensing, energy conversion, and storage [7]. Therefore, we will pick few examples taken from such a huge variety. For instance, the capability to controllably dope NWs is routinely exploited in field effect transistors [8] while the low mass peculiar to NWs renders them ideal to be used in cantilever force sensors [9] and the NW flexibility makes them easily integrable in devices like flexible displays and artificial skin [10]. Moreover, the NW diameter, smaller than the light wavelength in the visible range, allows NWs to confine electromagnetic waves in the radial direction while guiding light in the axial direction, a property that has been exploited to build NW‐based antennas, lasers, and light‐emitting diodes (LEDs). An example of a multicolor NW‐based LED is shown in Figure 3(a) [11]. In the field of energy conversion, we mention that the typically low thermal conductivity of NWs makes them ideal building blocks of thermoelectric devices able to convert wasted heat into electricity [12], while the high surface‐to‐volume ratio of NWs ensures great light absorption capability, which is currently exploited in the fabrication of high‐efficiency solar cells [13]. Finally, interfacing NWs with living cells for delivering drugs or doing sensing activity is a very fascinating field. As an example, in Figure 3(b) we show an array of NWs acting as force sensors for bacterial cell adhesion [14].
After this brief overview on the NW world, including growth processes and technological applications, we will describe the properties of NWs that can be addressed by Raman spectroscopy. Indeed, a deep understanding of the NW properties is the starting point to design powerful devices as well as to perform important fundamental physics studies.
2. Experimental setup for Raman spectroscopy in nanowires
Whenever an electromagnetic radiation heats a sample, the light interacts with the sample. It may be reflected, absorbed or scattered. Raman spectroscopy relies on inelastic scattering of the radiation by the sample. It is a versatile and nondestructive technique based on the interaction between the radiation and the vibrational and/or rotational motions of the ions and it provides information such as crystal symmetry, composition, strain, lattice dynamics, and electronic band structure. In a Raman experiment, a monochromatic light is usually sent on the sample and the scattered light is collected and analyzed. When the frequency of the scattered radiation is analyzed, there will be not only the incident radiation wavelength (elastic or Rayleigh scattering component) but also radiation scattered at frequencies lower (Stokes) or higher (anti‐Stokes) than the elastic one (inelastic scattering or Raman components). The intensity of the elastic component is much higher than the inelastic ones, thus special tricks are used to detect the weak Raman signal. Furthermore, the Stokes peak has intensity higher than the anti‐Stokes peak, and their intensities depend on the temperature. The inelastic peaks appear at frequencies that differ from the incident one by a quantity called Raman shift, independent of the excitation frequency. The Raman shift is the most significant information in a Raman experiment.
In a typical Raman setup, the excitation energy is provided by a monochromatic laser source emitting in the visible range (488, 514, and 633 nm are the most common wavelengths). The laser light is filtered by a laser band pass filter and its polarization is cleaned from possible depolarized contributions with the use of a polarizer. Then, the beam is guided toward the sample with a set of mirrors and a polarization preserving beam splitter (typically 50:50). If nanostructures are investigated, like in our case, the laser light is focused via a microscope objective. A good objective has a high numerical aperture (∼0.9 for 100× magnification), which results in a diffraction‐limited laser spot able to provide submicrometric resolution. The nanostructure is positioned on an
In Figure 4, a typical geometry for performing polarization‐resolved Raman measurements on a single NW is sketched. Let us consider a NW with zinc blende (ZB) phase, grown along the [111] direction and having a hexagonal cross section, with facets of the {110} family. After transferring the wire on a substrate, the flat facet of the family {110} is perpendicular to the incident light wavevector (
By measuring the dependence of the scattered intensity on the incident and scattered polarization directions one can deduce the symmetry of the Raman tensors, thus the symmetry of the corresponding phonon, based on the comparison with the theoretical calculation of the intensity of the Raman signal for that specific experimental geometry. The intensity of the scattered light
with
Once the basic principles of Raman spectroscopy in NWs and measurement setup have been summarized, the most significant results of Raman spectroscopy applied to NWs can be described.
3. Size effects in the Raman spectra of semiconductor nanowires
In a 3D‐crystal with N atoms per primitive unit cell, the phonon dispersion (namely, the relation between the frequency and the wavevector of lattice vibrations) is composed of 3N branches (three of them are acoustic and the remaining 3N−3 are optical). Along high‐symmetry directions the phonons are classified as transverse or longitudinal according to whether their displacements are perpendicular or parallel to the direction of the phonon wavevector
In nanostructured materials it is usually observed that the energy of TO and LO modes is very similar to the bulk case. Differences may arise due to phonon confinement effects when scaling down the size of the crystal. Indeed, whenever the sizes of the “phonon wave packet” are comparable to the crystal size, an uncertainty in wavevector is introduced, which results in a contribution to the Raman peak at frequencies different from that at the Γ point. In other words, there is a relaxation of the
In the context of size effects in NWs, in addition to phonon confinement also the high surface‐to‐volume ratio of NWs plays a role and creates differences with the bulk. As a matter of fact, the surfaces represent a new physical boundary. The crystal symmetry might be affected by the existence of the edges, which lead to a rearrangement of the lattice and can activate silent modes. Also, specific modes associated to the surface, such as surface optical (SO) modes or breathing modes, may appear [17]. The SO phonons are created at the interface between different materials with different dielectric constants and propagate along the interface. They are activated by a breaking of the translational symmetry of the surface potential, likely due to diameter variations along the NW length. Finally, since the surface atoms are “less bound” than the internal atoms, they “experience” a different local field. The propagation of optical phonons, where the oscillating dipoles, created by the out of phase oscillation of ions and cations, interact via a dipole‐dipole interaction, is most affected by this.
Besides the appearance of the SO modes, the peculiar cylindrical shape with nanoscale dimensions of the NWs gives rise to the so‐called dielectric mismatch effect, as will be discussed in the following. A representative example of the difference between NWs and the bulk is presented in Figure 6 for zinc blende GaAs [18, 19]. In panel (a) we show a Raman spectrum of a ZB NW grown along the [111] direction (blue) and a spectrum of a (111)‐oriented GaAs wafer (black) tilted by 90°. The spectra were, therefore, collected in the same scattering geometry, namely,
4. Assessment of the crystal phase of nanowires
The crystallization of NWs in a crystalline phase that is not stable in the bulk form is one of the consequences related to the large surface‐to‐volume ratio of NWs, since the “unusual” crystal structure formation is favored for certain ranges of the relevant interface energies. For instance, non-nitrides III–V materials (such as GaAs, InAs, InP, etc.) that are notoriously stable in the cubic ZB phase in the bulk form can crystallize in the hexagonal wurtzite (WZ) phase when grown in the NW form under suitable VLS conditions. The occurrence of WZ in the lattice of these NWs is one of the most surprising findings in NWs and it provided the unprecedented opportunity to investigate this poorly known crystal phase. Many studies indicate that the WZ phase is favored in NWs featuring a high surface‐to‐volume ratio, such as in small diameters NWs [22], but an exhaustive picture of the reasons why WZ is formed in NWs is still lacking in the literature. It is worth stressing that the electronic and optical properties of the NWs strongly depend on their crystal phase [23] and thus engineering the crystal phase switching leads to the realization of heterostructures with additional degrees of freedom enabling novel optoelectronic devices [24, 25].
The differences between ZB and WZ properties are given by their different crystal structures. The ZB crystal is formed by two interpenetrating face‐centered‐cubic Bravais lattices (each of a different atomic species), whereas WZ is constructed from two interpenetrating hexagonal‐close‐packed lattices. The differences between ZB and WZ crystals are best understood by observing their structures in the [111] direction (that is the [0001] direction in WZ, usually known as the
Figure 7(b) shows how the phonon dispersion of a III–V WZ crystal can be obtained by folding the one of the ZB structure along the [111] direction, namely from the Γ to the L point. We can consider only this high symmetry direction because we will deal with one‐phonon Raman scattering, which probes only phonons close to the Γ point. As discussed in the previous section for ZB GaAs crystals, there are six‐phonon branches: 2TA, 1LA, 2TO, and 1LO. We stress that the dispersion curves of the TA modes are relatively flat near the zone edge and their energies are much lower than the LA phonon energy due to the covalent nature of bonds in these crystals. The LO phonon has higher energy than the TO phonons near Γ due to the ionic character of the bonds and the macroscopic electric field connected with the long wavelength LO phonon, at variance with group IV crystals where they are degenerate because no extra charge is carried by the two identical atoms in the unit cell.
In WZ, four new modes appear at the Γ point of the Brillouin zone. The folded modes are indicated with red dashed lines. Group theory predicts eight‐phonon normal modes at the Γ point: 2A1 + 2E1 + 2B1 + 2E2. Considering our scattering geometry described in Figure 4 and the crystallographic axes of a typical WZ NW grown along the [0001] direction, only the A1(LO), E1(TO), E2H, and E2L modes can be experimentally observed. The atomic displacements associated to these modes are sketched in panel (c). The notation E1 and A1 denote modes vibrating perpendicular and along the growth axis, respectively. Since A1 and E1 modes are also found in ZB, the appearance of E2H and E2L modes in the Raman spectrum of III–V NW is the unambiguous signature of a WZ phase.
Polarization‐resolved Raman measurements provide a reliable way to address the crystal phase of a given NW. To obtain such information it is necessary to calculate the selection rules for the modes specific to that crystal phase by using Eq. (1) and compare them with the experimental results. The Raman tensors of all existing crystal structures can be found in [27]. As summarized in table I in [19], in WZ III–V NWs grown along the [0001] direction (parallel to the
5. Assessment of the chemical composition and strain field in nanowires
In order to demonstrate the power of Raman spectroscopy to probe the chemical composition of NWs, it is worth focusing on alloyed NWs, while to investigate the strain state heterostructured NWs (e.g., core‐shell NWs) are ideal. Here, we focus on core‐shell In
The chemical composition
In these NNs, the possible presence of strain was also probed by Raman spectroscopy. In Figure 9(b), we display spectra recorded in
In this section, it is also worth mentioning that Raman spectroscopy in semiconductor NWs may be used to monitor the incorporation of dopants. At variance with electrical measurements, Raman measurements are not affected by spurious effects coming from the fabrication of contacts. Information on the type and concentration of dopants can be obtained by measuring, respectively, the energy and the intensity of the local vibrational modes associated with the impurities. As an example, we mention Reference [29], where
6. Resonant Raman scattering in nanowires
In this section, we highlight the power of Resonant Raman scattering (RRS) to investigate the electronic band structure and the electron‐phonon interaction in semiconductor NWs. This investigation is possible because the scattering cross section contains the electron‐radiation and the electron‐phonon interaction Hamiltonians, as well as electronic states for electron‐hole pair. In standard conditions, it is very difficult to have access to this information, due to summation over all the intermediate states, but if resonant conditions are achieved, the excitation energy matches electronic interband transitions and the electronic‐related terms in the scattering cross section are sizably enhanced. Resonant conditions between excitation energy and electronic states may be reached by varying either the energy of the excitation (using a tunable laser) or the energy of the electronic states (for instance by applying an external pressure at fixed excitation energy). Indeed, the energy gap of semiconductors typically increases with pressure, thus if the pressure dependence of the energy gap is known, pressure‐dependent RRS measurements give information on the electronic band structure of the material. We will discuss both methods focusing on InAs NWs with WZ phase [30], because in III–V NWs with WZ phase the electronic band structure is poorly known and RRS has proved to be a necessary tool to shine light on this highly debated topic [31].
Figure 10(a) shows some spectra collected from a single WZ InAs NW with growth axis aligned with
These RRS data can be interpreted at the light of the following considerations. The three lowest energy electronic interband transitions in III–V WZ materials, labeled as A, B, and C, involve the bottommost conduction band minimum, having a
Let us now discuss high‐pressure Raman measurements on the same NWs [30, 32]. Measurements were performed by exciting bundles of NWs with 2.71 eV. Hydrostatic pressure was applied by using a screw clamped opposing‐plate diamond Anvil cell (DAC, as the one sketched in Figure 10(d)). The NWs were loaded together with a ruby microsphere in a sample chamber located in the center of a stainless steel gasket. A methanol‐ethanol mixture (4:1) was used as pressure transmitting medium, and the ruby microsphere was used for determining the pressure through the ruby‐fluorescence technique [33]. Raman spectra were collected in backscattering geometry without filtering light polarization, since it is not conserved through the diamond and anyhow the orientation of NWs in the bundle is unknown. Raman spectra collected from an InAs bundle are shown in Figure 10(c) for increasing applied pressure up to 8.5 GPa. At ambient pressure (0 GPa), the Raman spectrum is similar to the spectra in panel (a): the broad peak at ∼216 cm−1is due to convolution of the A1/E1 (TO) mode and the E2H TO mode (we continue to label the peak as TO), and the peak at ∼238 cm−1 is due to LO mode. We notice that the frequency of the TO and LO increases with pressure, the FWHM of the TO decreases with pressure, the intensity of the LO peak decreases after 3 GPa and vanishes for pressures higher than 6.4 GPa, and the intensity of the TO increases (with a first maximum around 4 GPa and a second one around 6.5 GPa) and then decreases drastically without vanishing. The absolute intensities of the TO and LO modes (after averaging between two different bundles) are plotted in panel (d) as a function of the applied pressure. Red circles refer to LO, black squares to TO. In bulk ZB InAs, the pressure at which the resonance is expected to occur (based on the known pressure dependence of the E1 band gap for 2.71 eV excitation energy) is ∼3 GPa, as indicated by a dashed line in panel (d). Here, the intensity increase for the TO mode is observed at a pressure slightly higher than 3 GPa due to a value of the E1‐gap slightly lower than the 2.71 eV. This finding confirms the results obtained by the energy‐dependent Raman study. Indeed, assuming for the E1 WZ band gap the same pressure dependence of the E1 ZB gap and an energy gap at ambient pressure of 2.4 eV as the one determined from data in Figure 10(b), the resonance is expected at about 4.2 GPa, in good agreement with the measurements. Moreover, the continuous decrease in intensity of the LO mode with pressure agrees with what expected from a gap which is already bigger than 2.71 eV at ambient pressure: with increasing pressure, and consequently increasing the relevant energy gap, the LO mode is going far and far from resonance conditions, leading to a continuously decreased intensity. This confirms its coupling with the gaps from the second and third valence bands at the A point. The disappearance of the LO mode at 6.4 GPa could be related to the structural phase transition that occurs in the ZB material, associated with the metallization of the system. We point out that the spectrum could be fully recovered after depressurizing the DAC, indicating a reversible structural transition.
We have shown that the present method, based on the combination of two RRS techniques, has proved to be a novel and powerful experimental tool for band structure investigation of nanoscale semiconductors.
In conclusion, we have provided valuable examples, mostly based on our experimental results, of how powerful is Raman spectroscopy in investigating all the most important aspects of the lattice dynamics of semiconductor nanowires.
Acknowledgments
The authors acknowledge S. Yazji and G. Abstreiter of Walter Shottky Institute of the Technische Universität München, A. Fontcuberta i Morral of the École Polytechnique Fédérale de Lausanne, and P. Postorino of Sapienza University of Rome for their precious contribution to data acquisition and interpretation. We acknowledge financial support from the Swiss National Science Foundation research grant (Project Grant No. 200021_165784).
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